Here is the problem with lumens, beside the fact colors may be slightly distorted in torch mode. Projectors output everything between white and black and million of shades of color in between. They do not produce blacks and dark colors any better no matter how many lumens you have because they do so by limiting light output, or in the case of black try and shut light output off totally. Simply put darks will look like the screen itself under whatever ambient light is striking it. Cranking up the bright end will cause more room reflections back to the screen brightening the darks and thus lower CR even more.
That said lumens are the fix but only IMHO when coupled to a darker neutral gray screen in applications such as yours. Your room is exactly the same as what I did in mine. It's a dual mode room with the ability for sports viewing with a comfortable amount of light on in the viewers end of the room and also functions well lights out more like a 120 plasma than a movie like image.
The key is all the above plus (gray). Darken the wall and ceiling close to the screen (about 5 feet out) control the lighting at the seating end intensity (dimmers) and also direction (spots not floods etc). Then get as much horsepower in the projector as you can and plan on attenuating a good amount of that light into the gray screen. In a room such as yours directional gain may or may not be your friend. If your viewing area is narrow then maybe add in a component of screen gain. But with a room that large I see people watching from lots of angles.
Also keep in mind things like sports and much of normal TV sitcom type images are full of high contrast ANSI like images. These type images lend themselves best to ambient viewing with a setup like this. The reason being much of the darks you will be seeing will be a form of perception of contrast in how our eyes adjust. If you try and watch a movie that contains lots of very dark images at night the perception will be lost due to the overpowering of the room lighting. It will still be better than with a brighter screen but you will be wanting for CR and shadow details.
Below is a test another member did showing how gray works.